Related papers: A Constraint Solving Approach to Tropical Equilibr…
We study tropical geometry in the global setting using Berkovich's deformation retraction. We state and prove the generalized balancing conditions in this setting. Starting with a strictly semi-stable formal scheme, we calculate certain…
We investigate the weak solvability of initial boundary value problems associated with an ecosystem model of the marine phosphorus cycle. The analysis covers the model equations themselves as well as their linearization which is important…
We discuss a novel analysis method for reaction network systems with polynomial or rational rate functions. This method is based on computing tropical equilibrations defined by the equality of at least two dominant monomials of opposite…
Reduction of combinatorial filters involves compressing state representations that robots use. Such optimization arises in automating the construction of minimalist robots. But exact combinatorial filter reduction is an NP-complete problem…
The performance of a constraint model can often be improved by converting a subproblem into a single table constraint (referred to as tabulation). Finding subproblems to tabulate is traditionally a manual and time-intensive process, even…
Finite-dimensional dissipative dynamical systems with multiple time-scales are obtained when modeling chemical reaction kinetics with ordinary differential equations. Such stiff systems are computationally hard to solve and therefore,…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
We develop a tropical analog of the simplex algorithm for linear programming. In particular, we obtain a combinatorial algorithm to perform one tropical pivoting step, including the computation of reduced costs, in O(n(m+n)) time, where m…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
While Robust Model Predictive Control considers the worst-case system uncertainty, Stochastic Model Predictive Control, using chance constraints, provides less conservative solutions by allowing a certain constraint violation probability…
The renormalization method which is a type of perturbation method is extended to a tool to study weakly nonlinear time-delay systems. For systems with order-one delay, we show that the renormalization method leads to reduced systems without…
Multiscale dynamics are frequently present in real-world processes, such as the atmosphere-ocean and climate science. Because of time scale separation between a small set of slowly evolving variables and much larger set of rapidly changing…
Robust Model Predictive Control (MPC) for nonlinear systems is a problem that poses significant challenges as highlighted by the diversity of approaches proposed in the last decades. Often compromises with respect to computational load,…
Inability of low-resolution ocean models to simulate many important aspects of the large-scale general circulation is a common problem. In the view of physics, the main reason for this failure are the missed dynamical effects of the…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
The tube model is a central concept in polymer physics, and allows to reduce the complex many-filament problem of an entangled polymer solution to a single filament description. We investigate the probability distribution function of…
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of…
We introduce a generalization of tropical polyhedra able to express both strict and non-strict inequalities. Such inequalities are handled by means of a semiring of germs (encoding infinitesimal perturbations). We develop a tropical…
This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed…
Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the…